{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example\n",
    "\n",
    "This produces Figure OA.1 in paper. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "taur = 0.6\n",
    "tauw = 0.3\n",
    "r = 0.03\n",
    "T = 65 - 30+1\n",
    "contrib = 1e3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def payout_tfsa(contrib,r,T,taur,tauw):\n",
    "    pay = contrib*(1.0+r)**T\n",
    "    return pay\n",
    "def payout_rrsp(contrib,r,T,taur,tauw):\n",
    "    pay = (contrib/(1.0-tauw)*((1.0+r)**T))*(1.0-taur)\n",
    "    return pay"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "taurs = np.linspace(0.0,0.8,1000)\n",
    "tfsas = [payout_tfsa(contrib,r,T,tau,tauw) for tau in taurs]\n",
    "rrsps = [payout_rrsp(contrib,r,T,tau,tauw) for tau in taurs]\n",
    "gain_dollars = [(f - a)/a*100 for f,a in zip(tfsas,rrsps)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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    "plt.figure()\n",
    "plt.plot(taurs-tauw,gain_dollars)\n",
    "plt.xlabel('MTR(retirement) - MTR(working)')\n",
    "plt.ylabel('pct increase in payout')\n",
    "plt.axvline(x=0.0,linestyle='--')\n",
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